(1) Field
The present invention relates to a system and method to efficiently approximate the term 2X.
(2) General Background
The function, f(X)=2X where X is a real number, is a common operation in computational applications. The term 2X can be expressed using the Taylor series as follows:                               2          X                =                              ∑                          N              =              0                        ∞                    ⁢                                           ⁢                                                    (                                  x                  ⁢                                                                           ⁢                  ln                  ⁢                                                                           ⁢                  2                                )                            N                                      N              !                                                          (        1        )            
Accordingly, 2X can be approximated by adding the first few elements of the sum expressed in equation (1). Since X is a real number, the process of approximating the term 2X would involve floating-point operations. Because operations on floating-point data are costly in nature, an efficient technique of approximating 2X would prove useful.